I treat all manner of vermin/insect in my home/studio as I would intruders. Go for the jugular. Swiftly.

I also had a glue-trap horror story - can't do those again!
 
There was also this time when we had one in our apartment and I happened to catch him by the front door (which was right next to the kitchen where he liked to hang out).  It was hilarious afterwards, because he KNEW he was caught so he just sat down and gazed up at me trying to look as cute as he could.  He didn't even freak out as I started to open the front door.  I literally told him "Ok, now out you go!" and he turned around and left!  My girlfriend at the time was watching from the living room and crying from laughing.  She said I wimped out, but it earned several brownie points at the same time. 
 
The "other" rodent story was a rat problem the apartment complex was having (same place as before down in Irvine California).  The maintenance guys had given us two huge rat traps to put out on the balcony near the palm trees.  One summer night, just as we were starting to drift off to sleep, we hear ***BANG!!!*** then this sickening flopping sound right outside our bedroom sliding glass door.  I looked at Michelle, she looked at me, then she said "Are you going to look?" Me: "Nope!" After a bit of prodding, I finally tilted a vertical blind slat out of the way but, fortunately, all I could see was an upside-down trap with a long tail coming out of it.  We let the maintenance guys deal with in the next morning - heh...

Oh yeah, +1 on the peanut butter if a hammer is not available.
 

One thing I'd add, if you're going to use the 'neck snapper' traps, put them in a shoebox or similar with a small hole big enough for the mouse. Mice can spring the trap and get a leg stuck in them and drag the trap off. I lost two traps like that, managed to retrieve one from under the cupboard floor with wriggling mouse attached, but the other one was nowhere to be seen.

Of course there's always cats. 
 

My friend Jami had mouse problems and used the old-fashioned traps.
She told me of one incident where the mouse didn't get completely into the trap and the bar chopped its snout off. She followed the trail of blood to find the creature behind her spice rack, writhing in pain. 
She switched to the 'catch and contain' traps after that.

I had good luck with electronic types of pest elimination as far as roaches go.  Not sure if they get rid of mice.

As a former rat owner/lover PLEEEEEASE do not use the glue traps!! They are extremely inhumane. They take way to long to kill the critters who in the meantime break/rip off their own legs tear off their fur/flesh trying to get away.
 
My old boss made me put them out (to my objections) and going around collecting them was awful. Sometimes just patches of fur and/or legs but no mouse. When he first bought them he was following me around making sure I was indeed putting them out. Within a couple minutes we heard some squeaking from the kitchen area and sure enough there was one in the trap struggling to get away. I grabbed it to put it out of it's misery and good ole bossy man snatched it out of my hands and said "No! Let the little [REDACTED] suffer!!" as he glared into its little eyes.
 
Eventually he wandered off. As soon as he did I went back, picked up the trap (with the mouse attached still struggling), put at the bottom of my big garbage can and chopped its head off with a sidewalk scraper.
 
Nasty. They also have a tendency to get stuck to wires, furniture, pets and anything else and the glue is a bugger to clean off.
 
The snappy traps are the way to go if you aren't willing to go the "catch and release" trap method. If you DO get the C&R route make sure you check them daily so they don't slowly starve to death (worse than just killing them) and when you release them you gotta do it waaaaaaay away from your house or they'll just come right back in. That of course is a pain in the butt and house mice likely won't do well in the wild (2nd gen onward) so snappy traps are the way to go IMO.
 
And yeah... peanut butter.
 
Also get a bunch of fine steel wool and plug up any holes/air gaps you can find. Mice/rats will chew/crawl through anything but the steel wool messes up their mouse and jabs their skin so they don't come through. For extra mouseproofing get sheets of aluminum (not foil) and attach them over said holes or even completely covere the bottom foot or so of your walls. They can't get through it at all.
 
So steel wool keeps the out of the walls and the aluminum sheets keep the from breaching the walls if they happen to make it through the mesh gauntlet.
 
I like mice too but they can get really out of control REALLY fast and poop/pee all over everything... which is icky.

We have trouble with outdoor rats chewing up the NOC lines on our vehicles (we park outdoors as the studio is our converted garage). It seems that rats are adverse to moth balls. Keeps them away. Maybe mice too?

Slugbaby
I used glue traps once, and it was heartbreaking.  I put them in a bucket of water to put them out of their misery as quickly as possible, but it was really traumatizing.

I euthanized my last rat by drawing it a warm bath and holding it under until it stopped moving. It had gotten really sick, really fast in the middle of the night (had a huge tumor on it's side) so I fed her strawberries (her favorite food) until she stopped licking the juice of my fingers then did the deed. Very sad.
 
Years later I asked my buddy who breeds/raises pet rats what he does/what is the most humane way and he said to put them in the freezer. They just go to sleep then freeze to death.